3.3
Norbert Wiener
In
1925 Norbert Wiener gave a talk in Goettingen. His talk was on quantum
physics, but he decided to use music as the principle upon which to base
it. Wiener gave detail on the relationship between time and frequency.
He proposed that to get a precise time would mean vagueness in pitch, and
vice versa. This is because whilst a note may be played for a certain amount
of time, the pitch produced relies on a different time line. He proposed
that if a 20Hz note is played for less than 1/20th of a second it will
produce no sound, just a small puff of air. You can't play a jig on the
lowest register of an organ. Things can only get so small before they cannot
exist. This argument was devised mainly to disprove the notion that a better
microscope would mean being able to see still smaller objects within smaller
objects 'ad infinitum'. (Wiener 1964: 544-546) This theory though has many
more applications to do with the aesthetic nature of granular synthesis.
Of course at this stage the term was not coined, but this idea has since
been introduced into the theory of granular synthesis. One cannot have
a grain that is smaller than the frequency it should contain. The size
of the grains and the number of grains would also determine what type of
sound could be produced.
At
this same time Jean Fourier was working on different ways to define sound.
He designed a method whereby any periodic signal could be reduced to sine
waves and analysed as such. He examined the relationship between sound
and pure sine waves which can be defined as three variables for each sine
wave: frequency, amplitude and phase (relative to the fundamental wave).
He theorised that any sound (assuming it had an infinite duration) could
be explained, or analysed in a series of sine waves of infinite duration.
The sine wave must have an infinite duration because it is an oscillation
that can never vary.
Fig 3.1: The composite wave (c), can be broken up into the sine waves (a) and (b), which can now be defined with just the three variables (although the phase is zero in this case. (Dodge & Jerse, Computer Music, page 47)
By
this definition of sound it was inferred that the converse was also true,
that any sound could be made up with the addition of various sine waves.
This would enable the reproduction of any sound or timbre (Dodge &
Jerse 1985: 47-49). The result would be a composite wave of a particular
timbre over an infinite duration.